Problem: Which of the following ordered pairs represents a solution to the equation below? $(-2, 1) (-1, -1) (0, 1) (1, 0) (2, -2)$ $y = -x-1$
Solution: We can try plugging in the x-value of each ordered pair into the equation. If we evaluate and get the y-value of the ordered pair, then that ordered pair is a solution! Let's consider $(-2, 1)$ If we plug in $-2$ for $x$ and evaluate, do we get $1$ $y = (-1)(-2) - 1 = 2 - 1 = 1$ Let's consider $(-1, -1)$ If we plug in $-1$ for $x$ and evaluate, do we get $-1$ $y = (-1)(-1) - 1 = 1 - 1 = 0$ Let's consider $(0, 1)$ If we plug in $0$ for $x$ and evaluate, do we get $1$ $y = (-1)(0) - 1 = 0 - 1 = -1$ Let's consider $(1, 0)$ If we plug in $1$ for $x$ and evaluate, do we get $0$ $y = (-1)(1) - 1 = -1 - 1 = -2$ Let's consider $(2, -2)$ If we plug in $2$ for $x$ and evaluate, do we get $-2$ $y = (-1)(2) - 1 = -2 - 1 = -3$ Thus the only ordered pair that is a solution to the equation is $(-2, 1)$ We come to the same answer by plotting the points and the equation. $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$ $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$